Physics graduate interested in doing research in PDE's.

[hawaiifiver]

Hello,

I've recently finished a degree in physics. I'm interested in partial differential equations. I was wondering what I could do for a MSc, because I don't think I want to do anything in physics. Maths has always appealed to me, so I was looking for some suggestions as to how I might get invloved in PDE research. How can I find out about topics of current research (can someone point me in the right direction, or give me a few examples). I ask this because I would like to put in some applications for MSc's by research. I don't think I want to do a taught MSc.

Thank you.

 

[bromden]

Well, I am no expert in the current trends in PDE research, but I will say that I know there are a couple of ways you can study them.

As you know, PDEs are quite different beasts than ODEs are, and finding general results about them is very difficult. Typically, you study certain classes of PDEs.

One way is by focusing on computational methods. In this vein, you focus on finding efficient and novel ways to numerically solve such equations.

The other way is to focus on analytic treatment of PDEs, which I imagine is done with more of a pencil-paper approach.

This publication seems to be pretty helpful, though certainly dated:

http://www.ams.org/publications/books/monographs/238preface

There is a download link at the bottom of the page. If some of the papers strike your fancy, take note of what Universities have, err, had groups doing such research. Then check out their websites to see if they are still active, or where there past members have gone.

Also, you may find better, more recent sources. I just ran a quick Google search on "current trends in PDE research" and that was one of the first results. You could spend some time scouring through search results.

 

[qspeechc]

Yes. If you want to study PDEs theoretically you do it through the mathematics department, in the field of analysis. http://en.wikipedia.org/wiki/Terence_Tao" is perhaps the most famous mathematician working in this field, in a famous department at UCLA for this type of research. Doing this type of theoretical research into PDEs requires an extensive background in pure mathematics, specifically analysis, you probably did not get in your physics degree.

Another angle to study PDEs from is the computational, where you look at approximate and numerical solutions, which means you also need to be a good programmer. This has more practical applications to physics and other sciences. This will be done under the Applied Mathematics department, in fact, in seems to me this is all they do in applied maths. Your physics degree is probably good preparation for this, because all or most of the important PDEs you will look at will be from physics.

You may want to speak to people from your university in both the Applied and Pure Mathematics faculties who work in PDEs or a related field (functional analysis, harmonic analysis, etc.)